ABSTRACT
The single-molecule electrophysiology procedure of monitoring the passage of macromolecules through a single pore is to measure the ionic current through the pore due to the transport of small electrolyte ions in the system under a voltage gradient. In general, when the macromolecules are either in the vicinity of the pore or inside the pore, the flow of small electrolyte ions through the pore is significantly modified, resulting in changes in the measured ionic current. When some monomers of the polymer are inside the pore, they exclude a certain number of the small ions that would have otherwise been present there, thus resulting in a reduction in the number of charge carriers in the electric field, as sketched in Figure 8.1. In this chapter, we describe the basic theoretical framework, called the Poisson-Nernst-Planck (PNP) formalism, to understand the key features of the measured open pore current and its modifications arising from the presence of macromolecules. Two kinds of situations, namely the equilibrium and the steady state, will be considered. In equilibrium, there is no net current flow, and the pore embedded inside amembrane develops an equilibrium membrane potential, called the Nernst potential, for a prescribed gradient in the electrolyte concentration across the pore, and vice versa. In the steady state, the net ionic current is a constant and time-independent, and we shall discuss this situation using the PNP formalism. For uniform electric fields across the pore, the steady-state situation in the PNP formalism reduces to analytical results known as the Goldman-Hodgkin-Katz (GHK) equations. After equipping with these classical theoretical procedures, we shall consider the effect of a polymer molecule on the ionic current through a pore and the role of fluctuations in the ionic current. Finally, we shall describe the electroosmotic flow (EOF) arising from the hydrodynamic flow of accumulated counterions near charge-bearing pore walls, which can play a major role in generating strong velocity fields in nanopores. These various components (PNP, GHK, and EOF) are required for interpreting the measured ionic currents in terms of molecular mechanisms.
